How often should I sprint in terror missions?
Solution 1:
Terror missions are somewhat unique in that you can get a general idea as to where the aliens are by where the civilians are dying - you can see the civilians even in the fog of war, and the aliens will be attracted towards them. During the alien turn you can also hear them screaming when they die - the camera tends to snap towards the civilians that are under attack.
Typically there are at least one group of chryssalids in a terror mission, which means that if you leave them alone for long enough, you're going to have big problems on your hands. Chryssalids also have no ranged attacks, which means that cover isn't a huge benefit against them.
My suggestion would be to try to move as fast as you can while still maintaining your defenses - if you don't have any idea where the aliens are, explore a couple of different directions early in your turn, while being ready to fall back if you encounter a particularly powerful alien group.
Remember that Assault troopers with Run and Gun can sprint and overwatch on the same turn, which can be powerful. Likewise, Support troops can get a boost to their ability to move without sprinting, which can make a difference. Snipers with squad sight should get to a vantage point early and try to inflict heavy damage as soon as possible.
Finally, don't neglect saving civilians, even if they're in an area with no aliens currently. Just moving within one square is enough to immediately remove them from the game. You don't need to cover their escape. This reduces the number of potential zombies/chryssalids and can keep your overall mission rating up without much effort.
Solution 2:
Don't overemphasize the importance of saving civilians. There are 3 categories on terror missions. If you can get 2 excellents on aliens killed and squaddies lost, it really doesn't matter too much if you get a poor from civilians killed.
What you really need to avoid, especially early, is the disaster missions where you wipe or at least lose multiple highly ranked soldiers. This can happen fairly easily if you go charging in trying to save civilians and suddenly get swarmed by Chryssalids.
Basically, I would go slightly out of my way to save a civilian, but not much. It's just not worth getting a soldier turned into a zombie to save a civilian. This means that I might sprint every once in a while, but mostly I play normally.
Solution 3:
I'm playing on classic difficulty, ironman on. I usually approach with the normal, defensive overwatch-stretches. If I do see a few chryssalids I might very well charge in to try to finish them off quickly. Just one getting away, turning civilians into unfriendly little things, is dangerous and might mean the wiping of the entire team. 6+ activated chryssalids is usually a recipe for disaster until much later in the game.
One more pointer: Bring lots of explosives on terror missions. If chryssalids manages to kill a civilian, it takes a turn for the transformation to happen. Hitting it immediately after with a grenade or rocket not only hurts it, it also destroys the body it just fed on. Problem solved easily. Since they haven't got weapons on them, no weapon fragments are lost by this approach, so the safeties on those alien grenades generally sits a bit more loose on my terror missions :-)
Solution 4:
Sprinting and ending up with a dead soldier for your troubles is a bad choice. Do not consider the civilians as being that important: the enemy kills them, that's bad. The enemy kills you, that's bad. You kill the enemy, that's good. No or less aliens means an easier claiming of civilians.
Do not underestimate snipers here, especially if you can toss those nifty "I see you" sucker bombs :P
Killing the enemy as prime goal saves more civilians. But they are randomly placed, so do not expect you can save all at every terror mission. Save your troops, kill the enemy, then save the civilians.